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An improved nonlinear conjugate gradient method with an optimal property

Kou Cai

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Abstract

Conjugate gradient methods have played a special role in solving large scale nonlinear problems. Recently, the author and Dai proposed an efcient nonlinear conjugate gradient method called CGOPT, through seeking the conjugate gradient direction closest to the direction of the scaled memoryless BFGS method. In this paper, we make use of two types of modified secant equations to improve CGOPT method. Under some assumptions, the improved methods are showed to be globally convergent. Numerical results are also reported.

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What this paper is about

Conjugate gradient methods have played a special role in solving large scale nonlinear problems. Recently, the author and Dai proposed an efcient nonlinear conjugate gradient method called CGOPT, through seeking the conjugate gradient direction closest to the direction of the scaled memoryless BFGS method. In this paper, we make use of two types of modified secant equations to improve CGOPT method. Under some assumptions, the improved methods are showed to be globally convergent. Numerical results are also reported.

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Available abstract

Conjugate gradient methods have played a special role in solving large scale nonlinear problems. Recently, the author and Dai proposed an efcient nonlinear conjugate gradient method called CGOPT, through seeking the conjugate gradient direction closest to the direction of the scaled memoryless BFGS method. In this paper, we make use of two types of modified secant equations to improve CGOPT method. Under some assumptions, the improved methods are showed to be globally convergent. Numerical results are also reported.

Key concepts: Nonlinear conjugate gradient method, Conjugate gradient method, Derivation of the conjugate gradient method, Broyden–Fletcher–Goldfarb–Shanno algorithm, Conjugate residual method, Mathematics, Gradient method, Nonlinear system

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